Volume 72, Issue 3

H/D and 12 C/ 13 C vapour pressure isotope effects (VPIEs) in liquid fluoroform (CHF 3 ) were studied at the MPW1PW91/6-31 ++ G( d ) level of theory. The CHF 3 monomer and CHF 3 molecules surrounded by other CHF 3 molecules in every direction in CHF 3 clusters were used as model molecules of vapour and liquid CHF 3 . Although experimental results in which the vapour pressure of liquid 12 CHF 3 is higher than that of liquid 12 CDF 3 and the vapour pressure of liquid 13 CHF 3 is higher than that of liquid 12 CHF 3 between 125 and 212 K were qualitatively reproduced, the present calculations overestimated the H/D VPIE and underestimated the 12 C/ 13 C VPIE. Temperature-dependent intermolecular interactions between hydrogen and fluorine atoms of neighbouring molecules were required to explain the temperature dependences of both H/D and 12 C/ 13 C VPIEs.

Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.

The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G = H [ G 1 , G 2 , …, G k ] be the generalised join graph of G 1 , G 2 , …, G k determined by H . In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of G′is${G'_i}s$ and H . Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when G′is${G'_i}s$ and H take some special graphs, such as the complete graph, the path, and the cycle.

The non-local residual symmetry for the classical Korteweg-de Vries equation is derived by the truncated Painlevé analysis. This symmetry is first localised to the Lie point symmetry by introducing the auxiliary dependent variables. By using Lie’s first theorem, we then obtain the finite transformation for the localised residual symmetry. Based on the consistent tanh expansion method, some exact interaction solutions among different non-linear excitations are explicitly presented finally. Some special interaction solutions are investigated both in analytical and graphical ways at the same time.

This article is a numerical investigation of boundary layer flow of nanofluid over a bended stretching surface. The study is carried out by considering convective mass flux condition. Contribution of viscous dissipation is taken into the account along with thermal radiation. Suitable similarity transformations are employed to simplify the system of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Computational results are extracted by means of a shooting method embedded with a Runge-Kutta Fehlberg technique. Key findings include that velocity is a decreasing function of curvature parameter K . Moreover, Nusselt number decreases with increase in curvature of the stretching surface while skin friction and Sherwood number enhance with increase in K .

This article reports a study on variable-generalised Chaplygin gas (VGCG) interacting with pressureless dark matter (DM) with interaction term Q chosen in the form Q =3 Hδρ Λ , where ρ Λ denotes the density of the VGCG. Detailed cosmology of the interacting VGCG has been studied and a quintom behaviour of the equation of state (EoS) parameter has been observed. A statefinder analysis has shown attainment of ΛCDM fixed point by the interacting VGCG. Subsequently, a reconstruction scheme for f ( T ) gravity has been presented based on the interacting VGCG with power-law form of scale factor. The EoS parameter corresponding to the reconstructed f ( T ) has shown quintom behaviour. Finally, we have studied the generalised second law (GSL) of thermodynamics in reconstructed f ( T ) cosmology considering the universe as a closed bounded system with future event horizon as the cosmological boundary. We have associated two different entropies with the cosmological horizons with a logarithmic correction term and a power-law correction term. We have studied the validity of the GSL for both of these corrections.

Recently, Maraj and Nadeem (E. N. Maraj, S. Nadeem, Z. Naturforsch. A 70 , 513 (2015)) discussed the application of Rabinowitsch fluid model for the mathematical analysis of peristaltic flow in a curved channel. The mathematical analysis presented by these authors is scrutinised in detail and certain subtle details are pointed out which affect the final results.

In this article we investigate the fluid flow through a thin fracture modelled as a fluid-saturated porous medium. We assume that the fracture has constrictions and that the flow is governed by the prescribed pressure drop between the edges of the fracture. The problem is described by the Darcy-Lapwood-Brinkman model acknowledging the Brinkman extension of the Darcy law as well as the flow inertia. Using asymptotic analysis with respect to the thickness of the fracture, we derive the explicit higher-order approximation for the velocity distribution. We make an error analysis to comment on the order of accuracy of the method used and also to provide rigorous justification for the model.

We perform a complete Lie point symmetry classification of the generalised foam-drainage equation and then construct an optimal system of one-dimensional subalgebra of the admitted symmetry operators and use them to reduce the equations under study. A power series solution of the reduced equation is constructed. Moreover, we find all multipliers of the equations and apply them to construct conservation laws.

In this article, a generalised Whitham–Broer–Kaup–Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham–Broer–Kaup–Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

We establish a discrete model for the Ablowitz–Kaup–Newell–Segur (AKNS) equation via generalised Cauchy matrix approach. Two semidiscrete AKNS equations are obtained by, respectively, introducing straight continuum limit and skew continuum limit. Some reductions are also discussed.